The 47 year old replaced Brendan Rodgers in February and guided the club to an eighth title in a row in his second stint in charge.
"When I was asked to take over, I felt it was my duty to do so," Lennon said.
"Celtic will always be my club and I wanted to help finish the job which had been started.
"I want to be part of delivering more of these great achievements and I look forward to working with the players, the staff and the fans to make this happen."
Lennon has signed a 12-month rolling contract, with John Kennedy continuing as assistant manager and Damien Duff retained as first-team coach.
"It is a massive honour," Lennon added. "I had always dreamed of returning to this role on a permanent basis and I am absolutely delighted to once again be part of one of the biggest and best clubs in the world - an institution which really does mean so much to me and one which has always been such a huge part of my life.
"In the space of just a few weeks, Trophy Day at Celtic Park and securing the treble treble at Hampden are two of my greatest days in football."
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